Multifractal analysis of Chinese stock volatilities based on the partition function approach

We have performed a detailed multifractal analysis on the 1-min volatility of two indexes and 1139 stocks in the Chinese stock markets based on the partition function approach. The partition function χq(s)χq(s) scales as a power law with respect to the box size ss. The scaling exponents τ(q)τ(q) form a nonlinear function of qq. Statistical tests based on bootstrapping show that the extracted multifractal nature is significant at the 1% significance level. The individual securities can be well modeled by the pp-model in turbulence with p=0.40±0.02p=0.40±0.02. Based on the idea of ensemble averaging (including quenched and annealed average), we treat each stock exchange as a whole and confirm the existence of multifractal nature in the Chinese stock markets.